An 800-metre-long train can pass a stationary pole completely in 72 seconds. A 1200-metre-long train can also pass a stationary pole completely in 72 seconds. If both the trains are running in the same direction, then the faster train, coming from behind the slower train, can cross the slower train in how much time?

An 800-metre-long train can pass a stationary pole completely in 72 seconds.

Speed of first train = $$\frac{length\ of\ train}{time}$$

= $$\frac{800}{72}$$

= $$\frac{100}{9}$$ m/s

A 1200-metre-long train can also pass a stationary pole completely in 72 seconds.

Speed of second train = $$\frac{length\ of\ train}{time}$$

= $$\frac{1200}{72}$$

= $$\frac{100}{6}$$

= $$\frac{50}{3}$$

Multiply by 3 in the numerator and denominator.

= $$\frac{150}{9}$$ m/s
If both the trains are running in the same direction, then the faster train, coming from behind the slower train, can cross the slower train in 't' seconds.

t = $$\frac{sum\ of\ the\ length\ of\ both\ trains}{speed\ of\ faster\ train - speed\ of\ slower\ train\ }$$

= $$\frac{800+1200}{\frac{150}{9}-\frac{100}{9}}$$

= $$\frac{2000}{\frac{50}{9}}$$

= $$\frac{2000\times\ 9}{50}$$

= $$40 \times 9$$

= 360 seconds